Matter coupled F(4) supergravity and the AdS6/CFT5 correspondence

F(4) supergravity, the gauge theory of the exceptional six-dimensionalAnti-de Sitter superalgebra, is coupled to an arbitrary number of vectormultiplets whose scalar components parametrize the quaternionic manifold$SO(4,n)/SO(4)\times SO(n)$. By gauging the compact subgroup $SU(2)_d \otimes\cG$, where SU(2)_d is the diagonal subgroup of $SO(4)\simeq SU(2)_L\otimesSU(2)_R$ (the R-symmetry group of six-dimensional Poincar\'e supergravity) and$\cG$ is a compact group such that $dim\cG = n$, we compute the scalarpotential which, besides the gauge coupling constants, also depends in nontrivial way on the parameter m associated to a massive 2-form $B_{\mu\nu}$ ofthe gravitational multiplet. The potential admits an AdS background for g=3m,as the pure F(4)-supergravity. We compute the scalar squared masses (which areall negative) and retrieve the results dictated by AdS_6/CFT_5 correspondencefrom the conformal dimensions of boundary operators. The boundary F(4)superconformal fields are realized in terms of a singleton superfield(hypermultiplet) in harmonic superspace with flag manifold SU(2)/U(1)=S^2. Weanalize the spectrum of short representations in terms of superconformalprimaries and predict general features of the K-K specrum of massive type IIAsupergravity compactified on warped $AdS_6\otimes S^4$.Comment: 21 pages, latex, minor corrections and reference adde